## Generalized analytic spaces, completeness and fragmentability.(English)Zbl 0995.54035

Summary: Classical analytic spaces can be characterized as projections of Polish spaces. We prove analogous results for three classes of generalized analytic spaces that were introduced by Z. Frolík, D. Fremlin and R. Hansell. We use the technique of complete sequences of covers. We explain also some relations of analyticity to certain fragmentability properties of topological spaces endowed with an additional metric.

### MSC:

 54H05 Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) 54F65 Topological characterizations of particular spaces 54C35 Function spaces in general topology 54D15 Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)
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### References:

 [1] Z. Frolík: Distinguished subclasses of Čech-analytic spaces (research announcement). Comment. Math. Univ. Carolin. 25 (1984), 368-370. [2] Z. Frolík: Generalizations of the $$G_\delta$$-property of complete metric spaces. Czechoslovak Math. J. 10 (85) (1960), 359-379. · Zbl 0100.18701 [3] Z. Frolík: A survey of separable descriptive theory of sets and spaces. Czechoslovak Math. J. 20 (1970), 406-467. · Zbl 0223.54028 [4] Z. Frolík: Čech-analytic spaces (research announcement). Comment. Math. Univ. Carolin. 25 (1984), 367-368. [5] R. W. Hansell: Descriptive Topology. Recent Progress in Recent Topology, North-Holland, Amsterdam, London, New York, Tokyo, 1992, pp. 275-315. · Zbl 0805.54036 [6] R. W. Hansell: Descriptive sets and the topology of nonseparable Banach spaces. Serdica Math. J. 27 (2001), 1-66. · Zbl 0982.46012 [7] R. W. Hansell: Compact perfect sets in weak analytic spaces. Topology Appl. 41 (1991), 65-72. · Zbl 0759.54016 [8] P. Holický: Čech analytic and almost $$K$$-descriptive spaces. Czechoslovak Math. J. 43 (1993), 451-466. · Zbl 0806.54030 [9] P. Holický: Zdeněk Frolík and the descriptive theory of sets and spaces. Acta Univ. Carolin. Math. Phys. 32 (1991), 5-21. · Zbl 0774.54025 [10] P. Holický: Luzin theorems for scattered-$$K$$-analytic spaces and Borel measures on them. Atti Sem. Mat. Fis. Univ. Modena XLIV (1996), 395-413. · Zbl 0870.54036 [11] J. E. Jayne, I. Namioka and C. A. Rogers: Topological properties of Banach spaces. Proc. London Math. Soc. 66 (1993), 651-672. · Zbl 0793.54026 [12] J. E. Jayne, I. Namioka and C. A. Rogers: Properties like the Radon-Nikodým property. Preprint. (1989). [13] J. E. Jayne and C. A. Rogers: $$K$$-analytic sets. Analytic Sets, Academic Press, London, 1980, pp. 1-181. [14] I. Namioka: Separate continuity and joint continuity. Pacific J. Math. 51 (1974), 515-531. · Zbl 0294.54010 [15] I. Namioka and R. Pol: $$\sigma$$-fragmentability and analyticity. Mathematika 43 (1996), 172-181. · Zbl 0858.46016 [16] I. Namioka and R. Pol: $$\sigma$$-fragmentability of mappings into $$C_p(K)$$. Topology Appl. 89 (1998), 249-263. · Zbl 0930.54018
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